1. Investigations in Number, Data, and Space: Teaching Philosophy

2. The Changing Face of Mathematics Instruction: What is different?  New roles for teachers and students  Teaching for understanding  All children can learn  Collaborative work  Alternative and multiple strategies

3. Organization of the Investigations Curriculum  Units (2- 6 weeks) – consists of several investigations on the same/similar topics  Investigations several sessions around A set of related problems Math relationships – building/constructing Games about particular mathematics Collecting, representing and interpreting data  Sessions – structure/learning cycle  Extensions & Excursions - differentiation

4. Learning Cycle  ENGAGE (hook; prior knowledge)  EXPLORE (hands on; experience)  EXPLAIN (term introduction)  EXTEND (yet another way)  EVALUATE (are learners getting the concept?) If YES, … If NO, …

5. The Mathematics Content  Number  Data  Geometry  Change

6. Special Features of the Investigations Curriculum  Materials  Technology  Cooperative learning and grouping  Assessment  Family connections  Review and practice  Support for Spanish-speaking students

7. The Teacher’s Role  Observe & listen carefully to students; Understand how students are thinking  Help students articulate their thinking, verbally & in writing  Establish a classroom atmosphere in which high value is placed on thinking hard about a problem  Insist that students keep track of their work and be able to explain or show their thinking  Ask questions that push students’ mathematical thinking further  Facilitate discussions about important math ideas  Make decisions about how to modify the curriculum appropriately for individuals or groups of students

8. Differentiating Instruction: Can we do it?  Everybody Counts (NRC, 1989)  Investigating real-life contexts  Linguistically diverse classroom Spanish vocabulary package Tips for linguistically diverse classroom Family letters (in six languages)  Investigating mathematical contexts

9. Differentiating Instruction: Process standards  Problem solving  Communication  Connections  Reasoning and proof  Representations